There are economic policies that can greatly mitigate this. Carbon taxes that subsidize sustainable projects, for one example.
And most of us, wealthy and poor, don't get to choose who creates our electricity
For what it's worth, this often isn't true. Here in NYC, for instance, electricity generation and transportation are somewhat independent markets. Any NYC resident can choose to change who actually supplies their electricity, and there are companies that guarantee renewable sources. It does, of course, cost more.